The integration of an electrical storage system (ESS) into a DC microgrid using a bidirectional DC/DC converter provides substantial benefits but requires careful design. Among such converter topologies, the Split-pi converter presents several merits at the cost of non-isolated operation. However, the few works in the literature on the Split-pi presented only closed-loop control with a single control loop; furthermore, they neglected the reactive components’ parasitic resistances and did not perform any experimental validation. This work aimed at investigating the use of the Split-pi converter as a power interface between an ESS and a DC microgrid. Five typical microgrid scenarios are presented, where each of which requires a specific state-space model and a suitable control scheme for the converter to obtain high performance. In this study, two different state-space models of the converter that consider the parasitic elements are presented, the control schemes are discussed, and criteria for designing the controllers are also given. Several simulations, as well as experimental tests on a prototype realized in the lab, were performed to validate the study. Both the simulation and experimental results will be presented in part II of this work. The proposed approach has general validity and can also be followed when other bidirectional DC/DC converter topologies are employed to interface an ESS with a DC microgrid.